prediction

via Bill McBride who got the non-taper right

Some thoughts from Alec Phillips at Goldman Sachs: Will the Federal Shutdown End with a Debt Ceiling Increase?   

In our view, the most likely outcome of the current fiscal dispute is an agreement that combines an increase in the debt limit and a "continuing resolution" that reopens the federal government. We would expect this to pass no earlier than the end of next week (i.e., October 11-12) and more likely sometime around the Treasury's projected deadline of October 17.

Other outcomes are possible, but we believe they have lower probabilities. It is possible that political pressure to end the shutdown could build, but polling thus far does not indicate this has happened yet. It is also possible that if the effort to resolve the two issues together fails, the shutdown could remain unresolved even after the debt limit has been increased. This is a possibility, but we see it as less likely than a combined continuing resolution and debt limit increase.

The intense public focus on the shutdown may have actually raised the possibility of a "clean" debt limit increase. While the situation could go a number of ways, it still appears that the risk of a failure to raise the debt limit is low and that the shutdown has not had a negative effect on the prospects for increasing it.  

And Phillips also mentions:  

Congress is scheduled to go on recess the week of October 13, but this would presumably have to be cancelled if the debt limit had not yet been addressed. In the past, seemingly intractable political disputes have often been resolved around the start of planned congressional recesses.
emphasis added

Can't miss recess ...